1. Field of the Invention
The present invention relates to a phototaking optical system using a diffractive optical element (DOE for short). More particularly, this invention is directed to a phototaking optical system designed for use on cameras such as silver halide or electronic cameras.
2. Discussion of Related Art
For phototaking optical systems designed for use on silver halide or electronic cameras, it has so far been proposed to improve their performance and cut down their cost. In regard to a general phototaking optical system, it is difficult to achieve cost reductions because many lenses are needed for achieving high performance by correcting aberrations. In recent years, therefore, cost reductions have been accomplished by reducing the number of lenses while keeping performance acceptable by the use of aspheric surfaces. However, aspheric surfaces have a grave disadvantage of being incapable of correcting for chromatic aberrations although they may correct monochromatic aberrations such as spherical aberrations, and coma. Therefore, an extreme reduction in the number of lenses for the purpose of achieving cost reductions often results in performance loss because chromatic aberrations become worse. To correct chromatic aberrations, there is thus no choice but to use suitable combinations of lenses of varying powers, but this inevitably incurs an increase in the number of lenses. That is, it is difficult to arrive at a sensible tradeoff between high performance and low cost.
Attention is now directed to a diffractive optical element (or DOE) having diffractive action to bend light rays. Unlike a general vitreous material, the DOE is characterized by having reciprocal dispersion, i.e., an Abbe number of -3.45, so that achromatization is achievable by a combination of positive power and positive power, unlike a conventional refractive system. Such a characteristic feature is believed to enable the DOE to be used with a phototaking optical system.
An account is here given of a DOE in general. The DOE is interpreted at great length in "Optics", Vol. 22, pp. 635-642, and pp. 730-737, for instance.
A conventional lens is based on refracting action at an interface of the medium, whereas the DOE is based on the diffraction of light. Now assume that light is incident on such a diffraction grating as depicted in FIG. 1. In general, the light leaving the grating upon diffraction then satisfies the following relation: EQU sin .theta.-sin .theta.'=m.lambda./d (a)
where .theta. is the angle of incidence, .theta.' is the exit angle, .lambda. is the wavelength of light, d is the pitch of the diffraction grating, and m is the order of diffraction.
Therefore, if a ring form of diffraction grating is designed to have a proper pitch according to equation (a), it is then possible to focus light upon one point. In other words, the diffraction grating is allowed to have lens action. Here, let r.sub.j and f represent the radius of a j-th grating ring and the focal length of a diffractive surface, respectively. If an optical path difference between a light ray diffracted by the j-th grating and a light ray passing through the center of the diffraction grating is designed to be integral multiples of wavelength, both light rays interact with each other to increase their intensity. That is, the following relation holds: EQU .sqroot.(r.sub.j.sup.2 +f.sup.2)-f=j.lambda. (b-1)
Also, if r.sub.j is not very large with respect to the focal length, the radius r.sub.j of the grating ring is then given by EQU r.sub.j =.sqroot.(2j.lambda.f) (b-2)
For the diffraction grating, several types are proposed, for instance, an amplitude modulation type made up of a bright-and-dark ring, and a phase modulation type with a variable refractive index or optical path length. In the amplitude type DOE, the ratio between the quantity of incident light and the quantity of light subject to first-order diffraction (hereinafter called diffraction efficiency), for instance, is at most about 6% because light of plural orders of diffraction is generated. The amplitude modulation type DOE, even when bleached or otherwise treated for diffraction efficiency improvements, has a diffraction efficiency of at most about 34%. However, the same phase modulation type DOE, if it is of a saw-toothed shape in section as depicted in FIG. 2, can have a diffraction efficiency increased to 100%. Such a DOE is called a kinoform. Here the height of each sawtooth is given by EQU h=m.lambda./(n-1) (c)
where h is the height of the sawtooth, m is the order of diffraction (hereinafter called the design order of diffraction), and n is the index of refraction of an optical member forming the diffractive surface.
As can be expected from equation (c) depending on wavelength, however, the diffraction efficiency of 100% is achievable for only one wavelength. Thus, the diffraction efficiency D.sub.M (.lambda.) depends on wavelength, and so is given by: EQU D.sub.M (.lambda.)=sinc.sup.2 [.pi.{M-m{(1-n)/(1-n.sub.DOE)}(.lambda..sub.DOE /.lambda.)](d)
where M is the order of diffraction at which the DOE is used, m is the design order of diffraction, .lambda. is the wavelength at which the DOE is used, .lambda..sub.DOE is the design wavelength, and n and n.sub.DOE are the indices of refraction of an optical member forming the diffractive surface at the wavelengths .lambda. and .lambda..sub.DOE.
A kinoform element, if it is to step approximation as depicted in FIG. 3, is often called a binary optical element, and can be relatively easily fabricated by lithographic techniques. The binary optical element is known to have a diffraction efficiency of 81%, 95%, and 99% according to 4-, 8-, and 16-step approximation, respectively.
Examples of such a DOE applied to phototaking optical systems are disclosed in the following publications.
WO95/18393 shows a phototaking optical system comprising a single lens and a diffractive surface for making correction for aberrations. JP-A 4-181908 discloses an easy-to-manufacture radial type inhomogeneous lens wherein the chromatic aberrations produced are set off and corrected by a diffractive lens. This inhomogeneous lens is made up of one to three lens elements. JP-A's 6-324262 and 6-331887 teach that a diffractive surface is formed on front lenses of telescopic systems to make correction for chromatic aberrations. The former system is made up of six lens elements, and the latter system is made up of 10 or 11 lens elements.
However, all these phototaking optical systems using DOEs are found to be still less than satisfactory in terms of performance and cost. The system disclosed in WO95/18393 is somewhat more inexpensive because of being a single lens, but its performance is insufficient because coma, and other aberrations remain under-corrected.
The system set forth in JP-A 4-181908 achieves high performance albeit being composed of a reduced number of lens elements. However, this system actually costs much because it uses an inhomogeneous lens. Inhomogeneous lenses are still unsuitable for mass production of cameras, etc., and so are unfavorable.
The systems set forth in JP-A's 6-324262 and 6-331887 achieve high performance by using DOEs for lenses in telescopic systems. However, these systems fail to take full advantage of DOEs because the DOEs are used only for the purpose of making fine correction for chromatic aberrations.
Thus, all these prior art arrangements fail to make a reasonable compromise between low cost and high performance.